Let G be a nontrivial connected graph of order n. Let k be an integer with 2 ≤ k ≤ n. A strong k-rainbow coloring of G is an edge-coloring of G having property that for every set S of k vertices of G, there exists a tree with minimum size containing S whose all edges have distinct colors. The minimum number of colors required such that G admits a strong k-rainbow coloring is called the strong k-rainbow index srx_k(G) of G. In this paper, we study the strong 3-rainbow index of comb product between a tree and a connected graph, denoted by T_n ⊳_o H. Notice that the size of T_n ⊳_o H is the trivial upper bound for srx₃(T_n ⊳_o H), which means we can assign distinct colors to all edges of T_n ⊳_o H. However, there are some connected graphs H such that some edges of T_n ⊳_o H may be colored the same. Therefore, in this paper, we characterize connected graphs H with srx₃(T_n ⊳_o H) = |E(T_n ⊳_o H)|. We also provide a sharp upper bound for srx₃(T_n ⊳_o H) where srx₃(T_n ⊳_o H) ≠ |E(T_n ⊳_o H)|. In addition, we determine the srx₃(T_n ⊳_o H) for some connected graphs H.